As emphasized in Ref. [1]}, the hybrid
model, already at leading-order,
takes into account radiative higher-order corrections associated with
extra hard emissions that are resummed by the gluon uPDF.
In the numerical calculations below the intrinsic charm PDFs are taken at the initial scale \(m_c= 1.3\)  GeV, so the perturbative charm contribution is intentionally not taken into account when discussing IC contributions.
